a) x - 2y = 3 x = 3 + 2y -2x + y = 0 -2( 3 + 2y) + y = 0 -6 - 4y + y = 0 -3y = 6 //: -3 y = -2 x = 3 + (-4) x = -1 B) 2x + y =9 y = 9 - 2x 5x - 4y = 3 5x - 4(9-2x) = 3 5x - 36 + 2x = 3 7x = 39 x = 5,(571428) y = 9 - 2 c) 2x - y = 4 -y = 2x - 4 y = -2x + 4 3x - 2y = 5 3x - 2(-2x +4) =5 3x + 4x -8=5 7x = 13 x=1,(857142)
a) { x-2y=3 { -2x + y=0 { x = 3 + 2y { -2 * (3 + 2y) + y = 0 { x = 3 + 2y { -6 - 4y + y = 0 { x = 3 + 2y { -3y = 6 /:-3 {y = -2 {x = 3 + (-4) = -1 b) { 2×+ y=9 { 5× - 4y=3 {y = 9 - 2x {5x - 4(9-2x) = 3 {y = 9 - 2x { 5x - 36 + 8x = 3 {13x = 39 x=3 y=9-6=3 c) { 3× ₋2y=5 { 2×₋y=4 -y = 4 - 2x y = 2x - 4 3x - 2(2x-4)=5 3x - 4x + 8 = 5 -x = -3 x = 3 y = 6-4=2 d) { 2×₊ 9y= ⁻9 { -3×₊3y=8 /:3 -x+y=8/3 y=8/3 + x 2x + 9(8/3 + x) = -9 2x + 24 + 9x = -9 11x = -33 x = -3 y=-1/3 e) { 2×₊3y=4 /:2 { 8×₋5y=-1 x = 2 - 3/2y 8(2-3/2y) - 5y = -1 16 - 12y - 5y = -1 -17y = - 17 y=1 x=2-1,5=0,5 f) { x₋y=0 { x₊y₊z=4 { x₊2y₊3z=9 x=y z=4-x-y x+2y+12-3x-3y=9 y+2y+12-3y-3y=9 -3y=-3 y=1 x=1 z=4-1-1=2
a){ x-2y=3 { -2x + y=0 {x=3+2y {-2x + y=0 -2×(3+2y)+y=0 -6-4y+y=0 -6-3y=0 -3y=6/÷(-3) y=-2 x=3+2y x=3+2×(-2) x=3-4 x=-1 {x=-1 {y=-2 b) { 2×+ y=9 { 5× - 4y=3 { y=9-2x {5x-4(9-2x)=3 5x-36+8x=3 5x+8x=3+36 13x=39/÷13 x=3 y=9-2x y=9-2×3 y=9-6 y=3 {x=3 {y=3 c) { 3× ₋2y=5 { 2×₋y=4 -y=4-2x/×(-1) y=-4+2x 3x-2×(-4+2x)=5 3x+8-4x=5 -x=5-8 -x=-3/×(-1) x=3 y=-4+2x y=-4+2×3 y=-4+6 y=2 {x=3 {y=2 d) { 2×₊ 9y= ⁻9 { -3×₊3y=8 2x=-9-9y/÷ 2 x=-⁹/₂-⁹/₂y -3×(-⁹/₂-⁹/₂y)+3y=8 ²⁷/₂+²⁷/₂y+3y=8 ²⁷/₂+²⁷/₂y+⁶/₂y=8 ³³/₂y=8-²⁷/₂ ³³/₂y=¹⁶/₂-²⁷/₂ ³³/₂y=-¹¹/₂/÷³³/₂ y=-⅓ x=-⁹/₂-⁹/₂×(-⅓) x=-⁹/₂+³/₂ x=-⁶/₂ x=-3 {x=-3 {y=-⅓ e) { 2×₊3y=4 { 8×₋5y=-1 2x=4-3y/÷ 2 x=2-³/₂y 8×₋5y=-1 -5y=-1-8x -5y=-1-8×(2-³/₂y) -5y=-1-16+²⁴/₂y -5y=-17+12y -15y-12y=-17 -17y=-17/÷(-17) y=1 x=2-³/₂y x=2-³/₂×1 x=2-³/₂ x=½ y=1 f) { x₋y=0 { x₊y₊z=4 { x₊2y₊3z=9 x=y podstawiam y za x w drugim równaniu y+y+z=4 2y=4-z/÷2 y=2-z/2 w trzecim rownaniu za y podstawiam 2-z/2, a za x y x₊2y₊3z=9 y+2(2-z/2)+3z=9 y+4-2z/2+3z=9 y+4-z+3z=9 y+4+2z=9 y+2z=9-4 znowu za y podstawiam 2-z/2 2-z/2+2z=5/×2 mnożąc przez 2, pozbywam sie mianownika 4-z+4z=10 3z=10-4 3z=6/÷3 z=2 teraz y y=2-z/2 y=2-²/₂ za z w liczniku podstawiam 2 y=2-1 y=1 y=x {x=1 {y=1 {z=2
